British and Irish Lions coach Warren Gatland has rallied behind embattled Australian counterpart Robbie Deans, highlighting the achievements of his fellow New Zealander as speculation mounts that he will be axed.

Deans' five-year reign will reportedly come to an end this week after his team's 41-16 thrashing by the Lions in the series-deciding third Test in Sydney.

He is contracted until the end of the year but his demise is being widely tipped with Reds boss Ewen McKenzie or the Brumbies' Jake White in line to take over before the start of the Rugby Championship next month.

The Sydney Morning Herald said Deans was due to meet with Australian Rugby Union (ARU) chief Bill Pulver on Monday morning.

"There has been a lot of emotion and comment expressed from various areas since Saturday's Test and we will not be entering into any speculation or debate on the coaching issue at this stage," said Pulver.

It's tough to have a Kiwi involved coaching an Australian side. I admire him for what he's achieved in rugby.

Warren Gatland on Robbie Deans

Gatland expressed empathy for Deans' plight.

"I've got a huge amount of respect for what Robbie's achieved in rugby," he told reporters in comments embargoed until Monday morning.

"I know it's been really tough for him being here. There's a lot of people split about whether he should carry on the job. There's been a lot of criticism.

"It's tough to have a Kiwi involved coaching an Australian side. I admire him for what he's achieved in rugby."

He added that he and Deans, the Wallabies' first foreign coach who has been in charge of a record 74-Tests since 2008, chatted after Saturday's game.

"He said he might get to see us in November but that depends on what happens in the next few weeks," said Gatland, who is also the coach of Wales, referring to the Wallabies' European tour later this year.

"I do feel for him and want to wish him all the best. I hope it works out for him."

Peter McGrath, the ARU chairman when Deans was hired and re-hired in 2011, also had words of encouragement, saying he had not received enough credit for his achievements.

''I personally think Robbie is a fantastic human being and has done a great service for Australian rugby,'' McGrath told the Herald.

''We were number five in the world when Robbie was appointed, we rose to number two and now we are number three. The board have to make a decision about how you get to number one - that is their task.''

Australia's next Test is against the world champion All Blacks in Sydney on August 17 - its opening match of the Rugby Championship, which includes South Africa and Argentina.

Deans has had a chequered history of success with the Wallabies with a 58 per cent success rate - winning 43 Tests and losing 29.

The team's failure to win on Saturday in what was deemed its most important match since the 2003 World Cup final means Deans still lacks a defining moment as Wallaby coach.

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